A box whose mass is 20 kg rests on a frictionless ramp with a 15 degree (upward) slope. A mover pulls up on a rope attached to the box to pull it up the incline. If the rope makes an angle of 40 degree with the horizontal, what force does the mover have to exert in order for the box to move up the ramp at a constant speed?
The compoment of the applied force F up the plane is F cos 25. With no friction, that must equal the weight component down the plane, which is M g sin 15 = 20*9.8* 0.2588
=50.7 Newtons
F = ?
I never asked this. Somebody else did.
Wrong
@David S. (Other): Stop, or you fight me.
@David S. (Other): I already took this profile so give yourself another one.
Hey. I'll take another profile instead. Keep it. Sorry.
Okay then. Sorry for being a bit rude.
To find the force that the mover has to exert in order for the box to move up the ramp at a constant speed, you can use the following steps:
1. Draw a free-body diagram of the box on the ramp. Label the weight of the box as mg, where m is the mass of the box and g is the acceleration due to gravity (9.8 m/s^2).
2. Break the forces into components parallel and perpendicular to the ramp. The weight mg can be broken into two components: mg sin(15°) acting down the ramp and mg cos(15°) acting perpendicular to the ramp.
3. Since the box is at a constant speed, there is no net force in the direction perpendicular to the ramp. Therefore, the perpendicular component of the weight force is balanced by the normal force from the ramp, and we can disregard it for this calculation.
4. The force that the mover exerts on the box is acting parallel to the ramp. Since we are given the angle between the force and the horizontal (40°), we need to find the component of the force that acts up the ramp.
5. The component of the applied force (F) up the ramp is given by F cos(25°), where 25° is the angle between the applied force and the horizontal. Set this equal to the weight component down the ramp: mg sin(15°).
6. Solve for F by rearranging the equation: F cos(25°) = mg sin(15°).
7. Substitute the given values into the equation: F cos(25°) = 20 kg * 9.8 m/s^2 * sin(15°).
8. Calculate the value of F: F = (20 kg * 9.8 m/s^2 * sin(15°)) / cos(25°).
9. Use a calculator to find the numerical value of F.
By following these steps, you can find that the mover has to exert a force of approximately 57.85 Newtons in order for the box to move up the ramp at a constant speed.