A crate of mass 100kg is at rest on a horizontal floor. The coefficient of static friction between the crate and the floor is 0.4, and the coefficient of kinetic friction is 0.3. A horizontal force, F, or magnitude 350N is applied to the crate. Which of the following is true?
A. The crate accelerates horizontally at 0.5m/s^2
B. The crate slides across the floor at .5m/s
C. The crate does not move.
Please give the correct answer and an explanation why it is correct.
max static friction force = .4*981
which is more than 350
so
It stays in place. 350 N might be enough to keep it moving, but is not enough to start it.
The correct answer is C. The crate does not move.
Explanation:
Static friction is the force that prevents an object from sliding when it is at rest. It acts in the opposite direction of any force applied to the object until the applied force is large enough to overcome the static friction force.
In this case, the applied force F is 350N. The maximum static friction force can be calculated by multiplying the coefficient of static friction (μs) with the normal force (N) exerted by the crate on the floor. The normal force is equal to the weight of the crate, which is given by the product of mass (m) and gravitational acceleration (g) (N = m * g).
Maximum Static Friction Force = μs * N
= μs * (m * g)
= 0.4 * (100 kg * 9.8 m/s^2)
= 392 N
Since the applied force of 350N is less than the maximum static friction force of 392N, the crate will not move. The static friction force will be equal and opposite to the applied force, preventing any motion.
If the applied force were greater than or equal to 392N, the crate would start moving, and the friction force would switch from static friction to kinetic friction. The coefficient of kinetic friction (μk) would then come into play. The crate would experience a different friction force, and it would begin to accelerate or slide across the floor. However, in this scenario, the applied force is not large enough to overcome the static friction force, so the crate remains at rest.
The correct answer is C. The crate does not move.
To understand why the crate does not move, we need to compare the applied force, F, with the maximum force of static friction that can be exerted between the crate and the floor.
The maximum force of static friction, Fs, can be calculated using the equation Fs = μs * N, where μs is the coefficient of static friction and N is the normal force. In this case, the normal force is equal to the weight of the crate, which is given by N = m * g, where m is the mass of the crate and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Substituting the given values, we get N = 100 kg * 9.8 m/s^2 = 980 N. And then substituting into the equation for static friction, we get Fs = 0.4 * 980 N = 392 N.
Since the applied force, F, is 350 N, which is less than the maximum static friction (392 N), the crate does not move. The static friction force prevents the crate from sliding, as long as the applied force is less than or equal to the maximum static friction.
Therefore, the correct answer is C. The crate does not move.