Anonymous
Anonymous asked in Science & MathematicsPhysics · 7 months ago

help in spring question physics?

A block of mass 1.5 kg is placed on a flat surface, and it is being pulled horizontally

by a spring with a spring constant 1.2 × 103 N/m  The coefficient

of static friction between the block and the table is µs = 0.60, and the coefficient of sliding

friction is µk = 0.40.

(a) By what amount must the spring be stretched to start the block moving?

(b) What is the acceleration of the block if the stretch of the spring is maintained at a constant value equal to that required to start the motion?

(c) By what amount must the spring be stretched to keep the mass moving at constant

speed?

Relevance
• Ash
Lv 7
7 months ago

(a) To start the block moving, the static friction should be overcome

spring force = Static frictional force

kx = μ(s)N

kx = μ(s)mg

x = μ(s)mg/k

x = 0.60*1.5*9.8/(1.2 x 10³)

x = 0.00735 m or 7.35 mm

The block should be stretched just over 7.35 mm to start moving

(b) F(net) = Spring force - Kinetic frictional force

ma = kx - μ(k)N

ma = kx - μ(k)mg

a = kx/m - μ(k)g

a = (1.2 x 10³)*(0.00735)/1.5 - 0.40*9.8

a = 2.0 m/s²

(c) To keep constant speed, the net force on the block must be 0

F(net) = Spring force - Kinetic frictional force

0 = kx - μ(k)N

kx = μ(k)mg

x = μ(k)mg/k

x = 0.40*1.5*9.8/(1.2 x 10³)

x = 0.0049 m or 4.9 mm

The spring should be kept stretched by 4.9 mm to maintain constant speed.