How can I solve for time in a pulley and ramp problem without a given variable?

In summary, the problem involves a 5kg mass on a frictionless ramp connected to a 10kg hanging mass by a cable passing over a pulley. Using the equation F=ma, the time it takes for the boxes to move 3m after being released from rest can be solved for. However, in order to solve for time in terms of seconds, another variable (such as the ramp angle) is needed. This can be solved using kinematic equations.
  • #1
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Homework Statement



A mass [itex]m{1}[/itex] = 5kg is on a frictionless ramp and connected to a cable that passes over a pulley which is then attached to a second hanging mass, [itex]m{2}[/itex] = 10kg. How long will it take the boxes to move 3m if they are released from rest?

[itex]F{A}[/itex]= Forces acting on hanging object
[itex]F{B}[/itex]= Forces acting on object on ramp

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Homework Equations



F=ma

The Attempt at a Solution



I have solved for T using the force equation on object A and got T= -m1a + 98N

Then I substituted for T in the equation for object B and solved for acceleration, yielding:a=(98N-49sin[itex]\vartheta[/itex])/15

My biggest problem is, the book says the answer is 1.13 seconds. How can I solve in terms of seconds without another variable provided? I can't think of a way to use elimination to solve for [itex]\vartheta[/itex].
 
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  • #2
The image didn't come out.

But as to your question - assuming your are given the ramp angle - hint: kinematic equations.
 

FAQ: How can I solve for time in a pulley and ramp problem without a given variable?

What is a pulley?

A pulley is a simple machine that consists of a wheel with a groove around its circumference and a rope or cable that runs through the groove. It is used to change the direction of a force and make work easier.

What is a ramp?

A ramp, also known as an inclined plane, is a flat surface that is tilted at an angle, allowing objects to be moved from a lower level to a higher level with less force.

How does a pulley and ramp work together?

A pulley and ramp work together to reduce the amount of force needed to lift or move an object. The ramp allows for a longer distance to be covered with less force, while the pulley changes the direction of the force, making it easier to lift the object.

What is the mechanical advantage of a pulley and ramp system?

The mechanical advantage of a pulley and ramp system depends on the number of pulleys and the angle of the ramp. Generally, the more pulleys and the longer the ramp, the greater the mechanical advantage. This means that less force is needed to lift or move an object.

What are some real-life applications of pulleys and ramps?

Pulleys and ramps are used in many different applications, such as elevators, cranes, and escalators. They are also commonly used in construction and transportation industries to move heavy objects or materials. In everyday life, pulleys and ramps can be found in simple machines like window blinds and garage doors.

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