A force of 1500 N (pull) is applied to a 200-kg crate at an angle of 20 degrees above horizontal. The coefficient of static friction is .65 and the coefficient of kinetic friction is .43. Does the crate move? If so, what is its acceleration?
first, does the horizontal pulling cause motion:
pulling force - retarding force=
1500cos20-.65(mg-1500sin30)=
so figure that out.
Next, if it is greater then zero, then
pulling force-movingretardingforce=ma
1500cos20-.43(mg-1500sin30)=ma
solve for a.
To determine whether or not the crate will move, we first need to calculate the maximum force of static friction.
The maximum force of static friction can be found by multiplying the coefficient of static friction (μs) by the normal force (N). The normal force is the force exerted by a surface to support the weight of an object lying on it.
Since the crate is on a flat surface, the normal force is equal to the gravitational force exerted on the crate, which can be calculated using the formula:
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).
N = 200 kg * 9.8 m/s^2
N = 1960 N
Now, we can calculate the maximum force of static friction (fs max) using the formula:
fs max = μs * N
fs max = 0.65 * 1960 N
fs max = 1274 N
Since the applied force of 1500 N (pull) is greater than the maximum static friction force of 1274 N, the crate will move.
To calculate the acceleration of the crate, we need to use the concept of net force. The net force acting on an object is equal to the force applied minus the force of friction.
The force of static friction is equal to the applied force in this case, so we can write:
fs = F - fk
Where fs is the force of static friction, F is the applied force, and fk is the force of kinetic friction.
The force of kinetic friction can be calculated using the formula:
fk = μk * N
fk = 0.43 * 1960 N
fk = 843.8 N
Now, we can calculate the net force:
fs = F - fk
1274 N = 1500 N - 843.8 N
Simplifying the equation, we find:
1274 N = 656.2 N
Since there is a net force of 656.2 N acting on the crate, we can calculate its acceleration (a) using Newton's second law:
F = m * a
a = F / m
a = 656.2 N / 200 kg
a = 3.281 m/s^2
Therefore, the crate will move with an acceleration of 3.281 m/s^2.