1. To move a large crate across a rough floor, you push on it with a
force F at an angle of 21° below the horizontal. The mass of the crate
is 32.0 kg. The coefficients of static and kinetic friction are 0.62 and
0.42 respectively.
(a) What force F is required to start the crate moving?
(b) If the force F is 365 N, the crate will move horizontally across the room. What is the acceleration?
i don't know HEEELLLPPPP
To solve this problem, we need to consider the forces acting on the crate and apply Newton's laws of motion.
(a) To determine the force required to start the crate moving, we need to overcome the static friction. The formula for static friction is given by:
Fs = μs * N
where Fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force acting on the crate.
First, let's calculate the normal force N. The normal force is the force exerted by the surface perpendicular to the crate.
N = mg
where m is the mass of the crate and g is the acceleration due to gravity.
N = 32.0 kg * 9.8 m/s^2 = 313.6 N
Next, we can calculate the force of static friction:
Fs = 0.62 * 313.6 N = 194.432 N
Since we want to start the crate moving, we need to apply a force larger than the force of static friction. Therefore, the force required to start the crate moving is greater than or equal to 194.432 N, but the exact value of F depends on the individual situation.
(b) To determine the acceleration of the crate when a force of 365 N is applied horizontally, we need to consider the forces acting on the crate during motion.
The force of kinetic friction is given by:
Fk = μk * N
where Fk is the force of kinetic friction and μk is the coefficient of kinetic friction.
Fk = 0.42 * 313.6 N = 131.712 N
Now, let's calculate the net force acting on the crate:
Net force (Fnet) = applied force - force of kinetic friction
= 365 N - 131.712 N
= 233.288 N
Since Fnet is the net force, we can use Newton's second law of motion to find the acceleration:
Fnet = ma
Where Fnet is the net force, m is the mass of the crate, and a is the acceleration.
233.288 N = 32.0 kg * a
Divide both sides of the equation by 32.0 kg:
a = 7.28 m/s^2
Therefore, when a force of 365 N is applied horizontally, the crate will have an acceleration of 7.28 m/s^2.