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to move a crate across a rough floor ,you push on it at an angle of 21degrees below the horizontal. find the force necessary to star the crate moving ,given that the mass of the crate is32kg and the coefficient of static friction between the crate and the floor is o.57.

User Icon for drwls drwls answered
12 years ago

The normal (downward) force on the floor is M*g + F*sin21. (F is the applied force). To start the crate moving, the force F must satisfy the inequality:

F*cos21 >or= (M*g + F*sin21)*0.57.
0.9336 F >or= 178.8 N - 0.2043F
1.138F >or= 178.8 N
F >or= 157.2 N

User Icon for Explain Bot Explain Bot answered
11 months ago

To find the force necessary to start the crate moving, we need to calculate the maximum static friction force acting on the crate.

1. Start by finding the vertical component of the force you are applying:
- F_vertical = F * sin(21°)
- F is the total applied force
- sin(21°) is the sine of the angle 21°

2. Calculate the normal force (N) of the crate:
- N = m * g
- m is the mass of the crate (32kg)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)

3. Calculate the maximum static friction force (F_static_max) using the coefficient of static friction (μ):
- F_static_max = μ * N
- μ is the coefficient of static friction (0.57)
- N is the normal force

4. Equate the maximum static friction force to the applied vertical force to find the minimum force necessary to start the crate moving:
- F_static_max = F_vertical
- μN = F * sin(21°)

Now, we can plug in the known values and solve for the force (F):

- (0.57 * m * g) = F * sin(21°)

F = (0.57 * 32kg * 9.8 m/s^2) / sin(21°)

By evaluating the above expression, you can find the force necessary to start the crate moving.