Force vs. Displacement graph question

[Plasm47]

In the graph below, forces labelled positive act in the direction of motion of the object, forces labelled negative oppose the motion. The object under consideration has a mass of 2.0kg and was initially at rest. Calculate its kinetic energy and speed when
a) d= 2.0m
b) d= 4.0m
c) d=6.0m
d) d= 8.0m

I know W is area under the graph, but not positive how to apply it. I assume the question is only asking for that moment in time, and NOT a time period.
so for (a) it would be W= 4.0N x 2.0m = 8J; which would also be E_k
and V= 2.83m/s
if this is correct then b and c follow the same method, so i got those right aswell.
Not sure of the procedure when the Force is negative.

 

[nasu]

No, this is not right. The kinetic energy at a given moment is equal to the work done from the beginning to that moment - given that it starts from rest so in the beginning has zero KE.
The work done can be calculated form the area under the curve, as you said (but did not do).

 

[Plasm47]

No, this is not right. The kinetic energy at a given moment is equal to the work done from the beginning to that moment - given that it starts from rest so in the beginning has zero KE.
The work done can be calculated form the area under the curve, as you said (but did not do).

okay, in that case:
a)to calculate work, solve for area under curve
W= l x w + (bXh)/2
W= 2m x 4N + (2m x (6N-4N)/2
W= 8J + 2J
w= 10 J
The E_k is equivilant to w since there is no work lost in the process.
E_k= 10J

now, solve for velocity
E_k= 0.5 (m)v²
v²= 0.5(2.0kg)/10J
v²= 0.1
v= √0.1
v=0.3m/s (to two sig digs)

if this is correct, then (b), (c), and (d) follow the same process

 

[nasu]

The value of the work looks OK.
Solving for v is not done properly (you can convince yourself calculating the KE with v=0.3m/s and m=2 kg).
Look again at the equation to solve.

 

[pmacias]

I would approach this question by first understanding the relationship between force and displacement. From the graph provided, it is clear that the object experiences a constant force of 4.0N in the direction of motion, resulting in a linear relationship between force and displacement.

To calculate the kinetic energy and speed of the object at different displacements, we can use the equations: Ek = 1/2mv^2 and v = √(2Ek/m), where m is the mass of the object.

For part (a), at a displacement of 2.0m, the object has a force of 4.0N acting on it in the direction of motion. Using the equation Ek = 1/2mv^2, we can calculate the kinetic energy as 8J. This is also the work done on the object, as work is defined as the product of force and displacement.

To calculate the speed, we can use the equation v = √(2Ek/m). Plugging in the values, we get a speed of 2.83m/s.

For parts (b), (c), and (d), we can follow the same procedure. Since the force is constant, the kinetic energy and speed will also be constant at each displacement. So for part (b), at a displacement of 4.0m, the object will still have a kinetic energy of 8J and a speed of 2.83m/s.

However, when the force is negative, it means that the force is acting in the opposite direction of motion. In this case, the work done on the object will be negative, as the force is opposing the motion. This means that the kinetic energy and speed of the object will decrease.

To calculate the kinetic energy and speed when the force is negative, we can use the same equations, but with a negative value for the force. For example, at a displacement of 6.0m, the force is -4.0N, so the work done on the object will be -8J. This means that the kinetic energy and speed will also be lower than in the previous cases.

In summary, to calculate the kinetic energy and speed of an object at different displacements, we can use the equations Ek = 1/2mv^2 and v = √(2Ek/m), and take into account the direction and magnitude of the force acting on the object.