Intro to Springs (Hooke's Law) Practice Problems

To investigate the spring constant of a bicycle shock absorber, a student used a spring balance and a calibration weight of 10 kg. The calibration weight is attached to the lower end of the scale. The calibration weight is placed carefully on the shock absorber. The length of the shock absorber is shortened by 7.0 cm and the spring balance shows a value of 42 N. Calculate the spring constant of the bicycle's shock absorber.

A 3.5 kg block when placed on a spring compresses it to 25 cm. The spring is 33 cm long and is placed vertically with one end fixed on the ground. Determine the spring constant.

A 1.25-kg cylinder rests at the upper free end of a vertical spring. The bottom of the ideal spring is tied to the earth. Determine the spring's compression if the spring constant is 375 N/m.

An ideal spring has an equilibrium length of 15 cm. The spring is suspended vertically from one of its ends. The spring's length extends to 18 cm when a calibration weight of 5 g is attached to the spring's lower end. Find the length of the spring when an additional 3 g is added to the spring's lower end.

An ideal spring is welded at one end to the smooth surface of a spin coater. The spring rests horizontally on the surface and has an equilibrium length of 14 cm. A small object of mass 55 g is fixed to the free end. The spin coater is rotated at a speed of 125 rpm. Once the object moves in a circular path at a constant speed, the spring length becomes 18 cm. Calculate the spring constant.

To illustrate a human soft tissue deformation, a science teacher uses two ideal springs and a small sphere. The sphere of mass m_s is attached to the free ends of the two springs. Then, the system is suspended vertically. The upper spring has an equilibrium length L_u and a spring constant k_u. The lower spring has an equilibrium length L_l and a spring constant k_l. The teacher fixes an additional small block of mass m_b to the free end of the lower spring. Find the expression of the system's total length.