an 88kg cardboard box is being pulled along a level floor. the coefficient of static friction between the box and the floor is 0.23, and the sliding friction is 0.12.
What is the weight of the box?
What force is needed to start the box moving?
What force is needed to keep the box moving at a constant velocity of 0.5m/s?
Once the box is moving what force must be applied to accelerate the box 2.5m/s/s?
a. Wb=m*g = 88kg * 9.8N/kg = 862.N.=Wt. of box.
Fb = 862.4 N. @ 0o. = Force of box.
Fp = 862.4*sin(00 = 0. = Force parallel to floor.
Fv = 862.4*cos(0) = 862.4 N. = Force perpendicular to floor.
Fs = u*Fv = 0.23*862.4 = 198.4 N.=Force
of static friction.
Fk = u*Fv = 0.12 * 862.4 = 103.5 N. =
Force of kinetic friction.
b. Fn = Fap-Fp-Fs = m*a.
Fap-0-198.4 = 88*0 = 0
Fap = 198.4 N. = Force applied to start
box moving.
c. Fn = Fap-Fp-Fk = m*a
Fap-0-103.5 = 88*0 = 0
Fap = 103.5 N. = Force applied to keep
box moving.
d. Fap-Fp-Fk = m*a.
Fap-0-103.5 = 88*2.5 = 220
Fap = 220 + 103.5 = 323.5 N.
To answer these questions, we need to understand a few key concepts. First, we need to know that weight is the force exerted by an object due to gravity. Weight can be calculated using the formula:
Weight = mass × acceleration due to gravity
The acceleration due to gravity on Earth is approximately 9.8 m/s^2.
Now, let's break down each question and find the answers step by step:
1. What is the weight of the box?
The weight can be calculated by multiplying the mass of the box by the acceleration due to gravity.
Weight = 88 kg × 9.8 m/s^2 = 862.4 N
2. What force is needed to start the box moving?
The force required to start moving an object is equal to the maximum static friction force that can be generated between the box and the floor. The formula to calculate the maximum static friction force is:
Maximum static friction force = coefficient of static friction × normal force
Here, the normal force is equal to the weight of the box because the box is on a level floor and there is no vertical acceleration or contact with any other surface. Therefore, the normal force is also 862.4 N.
Maximum static friction force = 0.23 × 862.4 N = 198.6 N
So, approximately 198.6 N of force is needed to start the box moving.
3. What force is needed to keep the box moving at a constant velocity of 0.5 m/s?
Once the box is moving and reaches a constant velocity, the force required to keep it moving is equal to the kinetic friction force between the box and the floor. The formula to calculate the kinetic friction force is:
Kinetic friction force = coefficient of kinetic friction × normal force
Here, the coefficient of kinetic friction is given as 0.12, and the normal force is still 862.4 N.
Kinetic friction force = 0.12 × 862.4 N = 103.49 N
So, approximately 103.49 N of force is needed to keep the box moving at a constant velocity of 0.5 m/s.
4. Once the box is moving, what force must be applied to accelerate the box 2.5 m/s^2?
To accelerate the box, we need to overcome the net force acting in the opposite direction. In this case, the net force is the difference between the applied force and the kinetic friction force.
Net force = applied force - kinetic friction force
Since we need to accelerate the box, the applied force should be greater than the kinetic friction force. Therefore, the formula becomes:
Applied force = kinetic friction force + mass × acceleration
Applied force = 103.49 N + 88 kg × 2.5 m/s^2 = 313.49 N + 220 N = 533.49 N
So, approximately 533.49 N of force must be applied to accelerate the box at a rate of 2.5 m/s^2.
I hope this helps! Let me know if you have any further questions.