A 1.8 kg breadbox on a frictionless incline of angle = 39 is connected, by a cor

Question

A 1.8 kg breadbox on a frictionless incline of angle = 39 is connected, by a cord that runs over a pulley, to a light spring of spring constant k = 120 N/m, as shown in the figure. The box is released from rest when the spring is unstretched. Assume that the pulley is massless and frictionless. (a) What is the speed of the box when it has moved 10.2 cm down the incline? (b) How far down the incline from its point of release does the box slide before momentarily stopping, and what are the (c) magnitude and (d) direction of the box's acceleration at the instant the box momentarily stops?

Explanation / Answer

here,

mass of the breadbox , m = 1.8 kg

theta = 39 degree

spring constant , k = 120 N/m

(a)

the speed of the box when it has moved 10.2 cm down the incline be v

using conservation of energy

m*g*h - 0.5 * k * x^2 = 0.5 * m * v^2

1.8 * 9.8 * 0.102 * sin(39) - 0.5 * 120 * 0.102^2 = 0.5 * 1.8 * v^2

v = 0.75 m/s

the speed of the box when it has moved 10.2 cm down the incline is 0.75 m/s

(b)

for the box to momentarily stops ,

using conservation of energy

m*g*h - 0.5 * k * x^2 = 0

1.8 * 9.8 * x * sin(39) - 0.5 * 120 * x^2 = 0

x = 0.19 m

the distance down the incline from its point of release does the box slide before momentarily stopping is 0.19 m

(c)

at this point

let the accelration be a

k*x - m*g*sin(theta) = m*a

120 * 0.19 - 1.8 * 9.8 * sin(39) = 1.8 * a

a = 6.5 m/s^2

the magnitude of accelration is 6.5 m/s^2

(d)

direction of the box's acceleration at the instant the box momentarily stops is upwards

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.