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2 years ago

3

Matt has a mass of 37 kg and skis down a hill with no friction or air resistance. The hill has an angle of 24 degrees. The free-

body diagram is show below.
a. Write the expression for the net force in the x-direction.

b. Write the expression for the net force in the y-direction.

c. What is the acceleration in the y-direction?

d. What is the normal force acting on him?

2 answers:

Pie2 years ago

6 0

a) mg cos(24)-N=0

b) mg sin(24)=ma

c) Since there is no original figure, in my coordinates a.y=0.

d) According to a): N=331.25 N

LUCKY_DIMON [66]2 years ago

4 0

Answer:

a) Along X direction since it can not move so Net force in x direction must be ZERO

$F_{net} = F_n - mgcos\theta$

since a = 0

$F_n - mgcos\theta = 0$

b)For Y direction net force is only due to component of the weight of object along the inclined plane

$mgsin\theta = F_{net}$

$m a_y = mgsin\theta$

c) for finding acceleration in Y direction we can use above equation

$m a_y = mg sin\theta$

divide both sides by mass

$a_y = g sin\theta$

$a_y = 9.8 sin24 = 3.98 m/s^2$

d) For finding Normal force we can use the expression of force in X direction

$0 = F_n - mg cos\theta$

$0 = F_n - (37\times 9.8\times cos24)$

$0 = F_n - 331.25$

$F_n = 331.25 N$

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