Force and Projectile Motion Questions

[Canadian]

Hello, I am in a introductory type first year physics class at univeristy.

Just got the midterm back, I got 80% (not too bad considering the class average was 55%).

Anyway there were two questions that I got completely wrong, not even a partial mark.

First Question: Part A:Consider a lawnmower of weight W which can slide across a horizontal surface with a coefficient of friction (mu) . In this problem the lawnmower is pushed using a massless handle, which makes an angle theta with the horizontal. Assume that , the force exerted by the handle, is parallel to the handle. Take the positive x direction to be to the right and the postive y direction to be upward. Find the magnitude of the force required to slide the lawnmower over the ground at constant speed by pushing the handle. Express the required force in terms of given quantities.

Part B:The solution for part a has a singularity (that is, becomes infinitely large) at a certain angle (theta "critical") . For any angle , the expression for F(handle) will be negative. However, a negative applied force F(handle) would reverse the direction of friction acting on the lawnmower, and thus this is not a physically acceptable solution. In fact, the increased normal force at these large angles makes the force of friction too large to move the lawnmower at all. Find an expression for tan(theta critical)

Question 2: Quarterback Fred is going to throw a pass to tight end Doug. Doug is 20 m in front of Fred and running straight away at 6.0 m/s when Fred throws the 500 g football at a 40 angle. Doug catches the ball without having to alter his speed and runs for the game-winning touchdown. How fast did Fred throw the ball?


For question one, I found the horizontal and vertical components of the pushing force set them to 0 and then set them equal to each other then solved for F, I think for this question I am missing something to do with the force of friction and how it is affected by the pushing handle. I didn't get part two.

For question 2 my scrap paper sheet was lost, so I'm not exactly sure what I did but the answer I got (was wrong) was that the speed of the ball was greater than 6 m/s. The marker wrote on the sheet that they were looking for a single numerical value.

Any help would be greatly appreciated, it's not worth anything now I just want to understand what I did wrong and what I should have done to solve the problems.

Thanks

 

[PhanthomJay]

Hello, I am in a introductory type first year physics class at univeristy.

Just got the midterm back, I got 80% (not too bad considering the class average was 55%).

Anyway there were two questions that I got completely wrong, not even a partial mark.

First Question: Part A:Consider a lawnmower of weight W which can slide across a horizontal surface with a coefficient of friction (mu) . In this problem the lawnmower is pushed using a massless handle, which makes an angle theta with the horizontal. Assume that , the force exerted by the handle, is parallel to the handle. Take the positive x direction to be to the right and the postive y direction to be upward. Find the magnitude of the force required to slide the lawnmower over the ground at constant speed by pushing the handle. Express the required force in terms of given quantities.

Part B:The solution for part a has a singularity (that is, becomes infinitely large) at a certain angle (theta "critical") . For any angle , the expression for F(handle) will be negative. However, a negative applied force F(handle) would reverse the direction of friction acting on the lawnmower, and thus this is not a physically acceptable solution. In fact, the increased normal force at these large angles makes the force of friction too large to move the lawnmower at all. Find an expression for tan(theta critical)

Question 2: Quarterback Fred is going to throw a pass to tight end Doug. Doug is 20 m in front of Fred and running straight away at 6.0 m/s when Fred throws the 500 g football at a 40 angle. Doug catches the ball without having to alter his speed and runs for the game-winning touchdown. How fast did Fred throw the ball?


For question one, I found the horizontal and vertical components of the pushing force set them to 0 and then set them equal to each other then solved for F, I think for this question I am missing something to do with the force of friction and how it is affected by the pushing handle. I didn't get part two.

For question 2 my scrap paper sheet was lost, so I'm not exactly sure what I did but the answer I got (was wrong) was that the speed of the ball was greater than 6 m/s. The marker wrote on the sheet that they were looking for a single numerical value.

Any help would be greatly appreciated, it's not worth anything now I just want to understand what I did wrong and what I should have done to solve the problems.

Thanks

For quiestion 1, originally Posted by Morsetlis,



Suppose there is a diagonal downward force from top right to bottom left on an object with weight w on a surface with coefficient of friction u (static/kinetic friction aren't distinguished in this question.)

The diagonal downward force is a vector F_h with angle theta to the horizontal.

I have already figured out that, for at a certain angle theta, the force F required to push the object to overcome its frictional resistance, is

F_h = (uw) / (costheta - usintheta)

However, since every positive change in angle will reduce the horizontal component and increase the vertical component, this will increase the effect normal force on the object, which is N = u + F_hsintheta, thus also increasing the frictional force, F_f = uN.

At a certain angle, called the Critical Angle, F_hcostheta, which is the horizontal force required to move the object, will be equal to F_f, the frictional force opposing F_h. Increasing that angle will leave F_h < F_f and the object will not be able to move. After a certain interval of increasing degree, F_h will be greater than F_f once more, but the object will now move in the opposite direction.

Knowing that the Critical Angle forms a singularity at F_h = (uw) / (costheta - usintheta) so that F_h goes to infinity, I know I have to solve for (costheta - usintheta) = 0.

However, I also need to know the tangent of the Critical Angle, and this is not a happy answer, since my answer for the Critical Angle also included arcsin functions.


Phantom says: I think i have read the problem corectly, and it appears that you have correctly solved part a, and that your only question relates to part b. You again are correct that solving (costheta =usintheta) will give the critical angle. Try dividing both sides of the equation by costheta to see what you get. What is sintheta/costheta equal to in terms of the trig identities?

This might help O Canada! but you need a good FBD to help explain it. Ask again if u need more help.

 

[kyle8921]

Hello,

Congratulations on your grade on the midterm! It sounds like you did well overall, but had some trouble with a couple of questions. Let's take a look at each question and break down the steps for solving them.

For the first question, it seems like you may have forgotten to include the force of friction in your calculations. Remember, the force of friction is always present when an object is sliding across a surface, and it is equal to the coefficient of friction (mu) multiplied by the normal force (which is equal to the weight of the object in this case). This force acts in the opposite direction of motion, so you will need to include it in your equations. Additionally, the force you calculated should be positive (since it is in the same direction as the motion), so there may have been a sign error in your calculations. As for part B, you will need to use the expression for the force of friction (mu * W) and set it equal to the force you calculated in part A. Then, solve for tan(theta critical).

For the second question, it seems like you may have made a mistake in your calculations or forgotten to include a key piece of information. Remember, the velocity of the ball after it is thrown will have both a horizontal and vertical component, and it will follow a parabolic trajectory due to the force of gravity. You will need to use the given information (distance, speed, angle) to solve for the initial velocity of the ball. It may be helpful to draw a diagram and break the velocity into its horizontal and vertical components.

Overall, it's important to carefully read the question and make sure you are including all relevant information and forces in your calculations. If you are unsure about a step or how to approach a problem, don't hesitate to ask your professor or a TA for clarification. Good luck with the rest of your course!