A few physics questions I'm having trouble with

Question

In the figure, a crate of mass m = 103 kg is pushed at a constant speed up a frictionless ramp (θ = 29°) by a horizontal force. The positive direction of an x axis is up the ramp, and the positive direction of a y axis is perpendicular to the ramp. (a) What is the magnitude of   ? (b) What is the magnitude of the normal force on the crate?

  

 

A dated box of dates, of mass 7.6 kg, is sent sliding up a frictionless ramp at an angle of θ to the horizontal. The figure here gives, as a function of time t, the component Vx of the box's velocity along an x axis that extends directly up the ramp. What is the magnitude of the normal force on the box from the ramp?

 

 

A block of mass m1 = 3.65 kg on a frictionless plane inclined at angle θ = 29.2° is connected by a cord over a massless, frictionless pulley to a second block of mass m2 = 2.44 kg hanging vertically (see the figure). (a) What is the acceleration of the hanging block (choose the positive direction down)? (b) What is the tension in the cord?

Answer 1

1. You didn't say what you want the magnitude of in question a. 

 

For question b...  Gravity exerts a downward force on the crate of mg = 103 * 9.8 = 1009.4 Newtons.  As you've described the axes, the normal force points in the positive y direction.  With a ramp angle of 29°, the normal force (i.e., the force on the crate, perpendicular to the ramp) is 1009.4 cos 29 = 882.8 N.

 

2. It's very similar to the first problem.  The velocity has nothing to do with the normal force, since the normal force acts in a direction perpendicular to the motion.  So as in the first problem, the normal force is just mg cos θ = 74.48 cos θ Newtons.

 

3. It's impossible to work this out without seeing the diagram.  Specifically, where is the pulley in relation to the first mass?  Is the cord parallel to the ramp?