An 58.0 N box of clothes is pulled 5.2 m up a 30.0° ramp by a force of 95 N that points along the ramp. If the coefficient of kinetic friction between the box and the ramp is 0.22, calculate the change in the box's kinetic energy.
uhm where did you get 57.5? and what is M & g????
The work done by the applied force is 95 x 5.2 = 494 J
Part of the work was done overcoming the friction force. The friction force is
Ff = 58*0.22*cos30 = 11.05 N and the work done against that force is 57.5 J
The work done increasing the gravitational potential energy is:
M*g*5.2*sin 30 = 150.8 J
That leaves a total of 494 - 57.5 - 150.8 J avaialbkle to increase kinetic energy
your awesome! but where did you get the 95 in the first equation?
95 N is the pulling force, which they tell you. That multiplied bhy the distance pulled is the work done by that force.
Thanks for the kind words; you'd better check my numbers anyway.
oh haha! sorry didn't see it
An 70.0 N box of clothes is pulled 24.0 m up a 30.0° ramp by a force of 115 N that points along the ramp. If the coefficient of kinetic friction between the box and ramp is 0.22, calculate the change in the box's kinetic energy.
To calculate the change in the box's kinetic energy, we first need to calculate the work done by all the forces acting on the box. The work done by a force can be calculated using the equation:
Work = Force * distance * cos(angle)
Let's calculate the work done by each force:
1. Gravitational force:
The gravitational force is acting downward, opposite to the direction of motion. So, the work done by the gravitational force is:
Work_gravity = force_gravity * distance * cos(180°)
Since the box is being pulled vertically upward, the angle between the gravitational force and the direction of motion is 180°. The gravitational force can be calculated using the formula:
force_gravity = mass * acceleration_due_to_gravity
Given that the box has a weight of 58.0 N, we can use the equation:
force_gravity = 58.0 N
Since the distance is 5.2 m and cos(180°) is -1, we can calculate the work done by the gravitational force:
Work_gravity = 58.0 N * 5.2 m * cos(180°) = -301.6 J
Note: The negative sign indicates that the work is done against the gravitational force.
2. Applied force:
The applied force is acting along the ramp, so the angle between the applied force and the direction of motion is 0°. Therefore, the work done by the applied force is:
Work_applied = force_applied * distance * cos(0°)
Given that the applied force is 95 N, the distance is 5.2 m, and cos(0°) is 1, we can calculate the work done by the applied force:
Work_applied = 95 N * 5.2 m * cos(0°) = 494 J
3. Frictional force:
The frictional force is acting opposite to the direction of motion, so the angle between the frictional force and the direction of motion is 180°. The frictional force can be calculated using the formula:
force_friction = coefficient_of_friction * force_normal
The force_normal is the normal force acting on the box, which is equal to the weight of the box.
force_normal = weight = 58.0 N
Given that the coefficient_of_friction is 0.22, we can calculate the frictional force:
force_friction = 0.22 * 58.0 N = 12.76 N
Since the distance is 5.2 m and cos(180°) is -1, we can calculate the work done by the frictional force:
Work_friction = force_friction * distance * cos(180°) = 12.76 N * 5.2 m * cos(180°) = -66.25 J
Note: The negative sign here indicates that the work is done against the frictional force.
Now, let's calculate the net work done:
Net Work = Work_applied + Work_gravity + Work_friction
= 494 J + (-301.6 J) + (-66.25 J)
= 126.15 J
The change in kinetic energy is equal to the net work done because work done is directly related to the change in kinetic energy. Therefore, the change in the box's kinetic energy is 126.15 J.