ohh sorry, in my first question...
A 15 kg box sits on a horizontal FORCE.
the coefficient of static fricition between the box and the surface is 0.70. if a force P is exerted on the box at an angle directed 37 degrees below the horizontal, what must be the magnitude of P to get the box moving??
``IT SHOULD BE A 15 kg box sits on a horizontal SURFACE and not A 15 kg box sits on a horizontal FORCE....
We did this problem for you below. I have a typo
force down is 15*9.8 not 15
WLS did it all out for you.
force down = 15 * 9.8 + P sin 37
force horizontal = P cos 37
0.7 (15 * 9.8 + P sin 37) = P cos 37
We both assumed that you meant horizontal surface.
ok...thanks a lot.....
No problem! To determine the minimum magnitude of force P required to get the box moving, we need to consider the forces acting on the box.
1. Weight (W): The weight of the box is given by the equation W = mg, where m is the mass of the box and g is the acceleration due to gravity. In this case, the mass of the box is 15 kg, so the weight W = 15 kg * 9.8 m/s².
2. Normal force (N): The normal force is the force exerted by the horizontal surface on the box perpendicular to the surface. Since the box is initially at rest, the normal force is equal in magnitude and opposite in direction to the weight of the box (N = -W).
3. Frictional force (Ff): The frictional force opposes the motion of the box and prevents it from sliding initially. The maximum static frictional force (Ffs) can be calculated using the equation Ffs = µs * N, where µs is the coefficient of static friction and N is the normal force.
4. Applied force (P): The force P is exerted at an angle of 37 degrees below the horizontal. To determine the horizontal component of this force (Pcosθ), we multiply the magnitude of the force P by the cosine of the angle.
To get the box moving, the applied force P must overcome the maximum static frictional force Ffs. Therefore, we need to find the minimum magnitude of P that exceeds Ffs.
Now, using the given numbers, we can solve for P.
1. Calculate the normal force N: Since the box is on a horizontal surface, N is equal to the weight of the box. N = -W.
2. Calculate the maximum static frictional force Ffs: Ffs = µs * N.
3. Calculate the horizontal component of the applied force P: Pcosθ = P * cos(37°).
4. Set up the equation to determine the minimum magnitude of P: Pcosθ = Ffs.
5. Rearrange the equation to solve for P: P = Ffs / cos(37°).
Substitute the values of Ffs and N calculated in the previous steps into the equation, and you can find the minimum magnitude of P required to get the box moving.