Multiple Choice
A 1.0 m-long spring is laid horizontally with one of its ends fixed. When you pull on it with 50 N, it stretches to 1.2 m. (a) What is the spring's force constant (b) How much force is needed to compress it to 0.7 m?
17. Periodic Motion
Spring Force (Hooke's Law)
Struggling with Physics?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
A 1.1 m length of string has a radius of 1.2 mm. It stretches by 1.2 cm when a 5.6 kg mass is suspended from it. What is Young's modulus of the rope?
A
B
C
D
E
Verified step by step guidance1
First, understand that Young's modulus (E) is a measure of the stiffness of a material. It is defined as the ratio of tensile stress to tensile strain. The formula for Young's modulus is: , where F is the force applied, A is the cross-sectional area, ΔL is the change in length, and L is the original length.
Calculate the force (F) exerted by the mass using the formula: , where m is the mass (5.6 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²).
Determine the cross-sectional area (A) of the string using the formula for the area of a circle: , where r is the radius of the string (1.2 mm converted to meters).
Calculate the tensile strain, which is the ratio of the change in length (ΔL) to the original length (L). Here, ΔL is 1.2 cm converted to meters, and L is 1.1 m.
Substitute the values of F, A, ΔL, and L into the Young's modulus formula to find E. This will give you the stiffness of the rope, which you can compare to the given options to identify the correct answer.
5:37mWatch next
Master Spring Force (Hooke's Law) with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice
Spring Force (Hooke's Law) practice set
Problem sets built by lead tutorsExpert video explanations