A runner moving at a speed of 12 m/s rounds a bend with a radius of 20m. (a) Fin

Question

A runner moving at a speed of 12 m/s rounds a bend with a radius of 20m. (a) Find the centripetal acceleration of the runner. (b) Which of the forces listed below supplies the force needed to give this acceleration to the runner? Normal___ Friction___ Weight___ Tension___ Centripetal___ Two forces act on a 6.0-kg block resting on a frictionless surface as shown. What is the magnitude of the horizontal acceleration of the block? A projectile of mass 2 kg is shot straight up with an initial speed of 18.0 m/s. (a) Use conservation of energy to find how high would it go if there were no air resistance? (b) If the projectile rises to a maximum height of 12 m, the magnitude of the average force due to air resistance.

Explanation / Answer

5. (a) the formula for centripetal acceleration
a = v²/r
= 12^2/20

= 7.2 m/s^2

(b) Friction exerts the force.

6.the net horizontal force is

Fx = 3.7 + 5.9×cos (43)

= 8.014 N

The horizontal acceleration is

a = Fx/m

= 8.014/6.0

= 1.335 m/s^2

7.(a) conserving energy, initial K.E = P.E
0.5m×v^2 = m×g×h
so, h = v^2/2g = 18^2/(2*9.8) = 16.530 m

(b) by work energy principle,
initial K.E = P.E + work done by air resistance for 12 m
0.5×mv^2 = mg×12 + F×12
so, 0.5×2×18^2 - 2×9.8×12= F×12
F = 7.4 N

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