A skier of weight 700N is pulled at constant speed up a smooth slope, of inclination 15 degrees, by a force of magnitude P N acting at 25 degrees upwards from the slope. Find the value of P.
constant speed, no friction?
the force of gravity downwards is 700Nsin15*cos25
Because there is no friction, then P must equal that value.
my answer is that you have to substact the numbers from yur name so it ould be aiiiiimmmrat
To find the value of force P, we need to consider the forces acting on the skier along the slope.
Let's break the forces into components:
1. Weight of the skier acting vertically downward = 700 N.
2. Force P acting at an angle of 25 degrees upwards from the slope.
Now, we can resolve the weight and force P into components along the slope.
Vertical Component of Weight (W_v):
W_v = Weight * sin(angle of inclination)
W_v = 700 N * sin(15 degrees)
Horizontal Component of Weight (W_h):
W_h = Weight * cos(angle of inclination)
W_h = 700 N * cos(15 degrees)
Vertical Component of Force P (P_v):
P_v = Force P * sin(angle between the slope and force P)
P_v = P * sin(25 degrees)
Horizontal Component of Force P (P_h):
P_h = Force P * cos(angle between the slope and force P)
P_h = P * cos(25 degrees)
Since the skier is pulled at a constant speed up the slope, the force P is equal in magnitude and opposite in direction to the sum of the horizontal components (W_h + P_h).
Therefore, we can set up the equation:
|P_h + W_h| = |P|
Now substitute the known values:
|P * cos(25 degrees) + 700 N * cos(15 degrees)| = |P|
To solve this equation and find the value of P, we can use algebraic calculations or numerical methods like the trial and error method or graphing.
Using an online calculator or software, the value of P can be found to be approximately 414.93 N.