1. A student is dragging a 5 kg box along the floor. He pulls on the rope with a 25 Newton force. The rope is 37 degrees above horizontal. As the box slides 10 meters, it goes from a speed of 3 m/s to a speed of 7 m/s.
a.) calculate the normal force on the box
b.) calculate the work the rope does on the box
c.) Calculate the box’s change in kinetic energy
d.) Calculate the work that friction does on the box.
e.) Calculate the force of friction on the box.
f.) Calculate the coefficient of sliding friction between the box and the floor.
g.) Calculate the student’s power.
normal force on box: mg-25sin37
work done by rope: 25cos37*10+1/2 m(7^2-3^2) that is the work done by the pulling plus the change in KE.
I will be happy to critique your work.
To solve these problems, we need to use various formulas and concepts from physics. Let's go through each question step by step:
a) To calculate the normal force on the box, we need to consider the vertical forces acting on the box. The normal force is equal to the weight of the box, which is given by the formula:
Weight = mass * gravity
Given that the mass of the box is 5 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight:
Weight = 5 kg * 9.8 m/s^2
b) The work done by the rope on the box can be calculated using the formula:
Work = force * distance * cos(theta)
Where force is the applied force (25 N), distance is the displacement of the box (10 m), and theta is the angle between the applied force and the displacement (37 degrees above horizontal).
Work = 25 N * 10 m * cos(37 degrees)
c) The change in kinetic energy (delta KE) of the box can be calculated using the formula:
delta KE = 1/2 * mass * (final velocity^2 - initial velocity^2)
Given that the mass of the box is 5 kg, the final velocity is 7 m/s, and the initial velocity is 3 m/s:
delta KE = 1/2 * 5 kg * ((7 m/s)^2 - (3 m/s)^2)
d) The work done by friction on the box can be calculated using the formula:
Work = force of friction * distance
e) To calculate the force of friction on the box, we can use the formula:
Force of friction = coefficient of friction * normal force
f) To calculate the coefficient of sliding friction, we can rearrange the formula for the force of friction:
Coefficient of sliding friction = force of friction / normal force
g) The student's power is given by the formula:
Power = work / time
Where work is the work done by the rope on the box, and time is the time taken for the box to slide the given distance.
I hope this explanation helps you understand how to solve each part of the problem.