Question

A customer sits in an amusement park ride in which the compartment is to be pulled downward in the negative direction of a y axis with an acceleration magnitude of 1.24g, with g 9.80 m/s2 . a 0.567 g coin rests on the customer’s knee. once the motion be- gins and in unit-vector notation, what is the coin’s acceleration rel- ative to (a) the ground and (b) the customer? (c) how long does the coin take to reach the compartment ceiling, 2.20 m above the knee? in unit-vector notation, what are (d) the actual force on the coin and (e) the apparent force according to the customer’s meas- ure of the coin’s acceleration?

Answer 1

a) g = -9.8*j m/s^2

b) g = 2.35*j m/s^2

c) t = 1.37 s

d) F = - 5.56x10^-3 N*j

e) F = 1.33x10^-3 N

Step-by-step explanation:

a) According to the exercise, the acceleration of the compartment is equal to:

g = -9.8*j m/s^2

b) The acceleration of the currency to the client will be equal to:

a = -1.24*g*j

F = -(m*a)

F = -(-1.24*g*j)*m = 1.24*g*j*m

The net force on coin is equal to:

Fnet = F + W = 1.24*g*m*j - m*g*j = 0.24*g*m*j

dividing the equation over m:

Fnet/m = (0.24*g*m*j)/m = 0.24*g*j = 2.35*j

c) The time it ta)akes for the coin to reach the ceiling of the compartment at a distance of 2.2 m can be calculated using the following equation:

s = u*t + (a*t^2)/2

Clearing t:

t = ((2*s)/a)^1/2 = ((2*2.2)/2.35)^1/2 = 1.37 s

d) The force on the coin is equal to:

F = -m*g, m = 0.567 g = 5.67x10^-4 kg

F = -5.67x10^-4 * (9.8*j) = - 5.56x10^-3 N*j

e) The apparent force is calculated with the following equation:

F = ma = (5.67·10^-4 kg)·(2.352 m/s²) = 1.33x10^-3 N

Answer 2

(a) The coin is accelerated only by gravity (until it hits the ceiling). Its acceleration is -9.80 m/s²

(b) The acceleration relative to the customer is
(-1.0 g) - (-1.24 g) = 0.24 g ≈ 2.352 m/s²

(c) The distance (d) covered is
1/2at² = d . . . . for some acceleration a
2.2 m = (1/2)(2.352 m/s²)t²
Solving for the time to cover the distance, we get
t = √(2·2.2/2.352) s ≈ 1.368 s

(d) The actual force on the coin is that due to gravity, as found in part (a). (The first m is "mass"; the second m is "meters".)
F = mg = (5.67·10^-4 kg)·(-9.8 m/s²) = -5.5566·10^-3 N

(e) From the customer's point of view, the apparent force on the coin is
F = ma = (5.67·10^-4 kg)·(2.352 m/s²) = 1.333584·10^-3 N
(The positive sign means directed upward.)