Question

A ski and its skier, with a total mass of 97 kg, emerge from a downhill track onto a horizontal straight track with an initial speed of 56 m/s. If a force slows them to a stop at a constant rate of 3.0 m/s2, (a) what magnitude F is required for the force, (b) what distance d do they travel while slowing, and (c) what work W is done on them by the force? What are (d) F, (e) d, and (f) W if they, instead, slow at 6.0 m/s2?

Answer 1

Answer:

A. -291 N.

B. 5.2 km.

C. 1.5*10⁶ J.

D. -291 N.

E. 1.5*10⁵ J.

Explanation:

Given,

Mass (m) = 97 kg

Initial Velocity (u) = 56 m/s

Final Velocity (v) = 0 m/s

Acceleration (a) = -3 m/s²

A. Force = ma

= [97 * (-3)] N

= -291 N

(Negative force means that the force must be applied on the opposite direction of the object moving)

B. Let the Distance be S.

= v² = u²-2aS

= 0² = 56² - 2(3S)

= 0 = 3136 - 6S

= 6S = 3136

= S = 5226.6 m or, 5.2 km

C. Work Done = F*s

= (-291*5226.6) J                

= 1.5*10⁶ J

(Negative work means object slows down)

D. (-291) N

E. If,

Acceleration (a) = -6 m/s²

Force = ma

= 97*(-6) N

= -582 N

= Distance = v² = u²-2aS

= 0 = 56² - 2(6S)

= 0 = 3136 - 12S

= 12S = 3136

= S = 261.3 m or, 0.26 km

Work Done = F*s

= [-582*261.3] J

= 1.5*10⁵ J

Hope this helps.