Questions: Two carts with masses m₁=100 kg and m₂=50 kg are connected by the rope at the applied force of Fₐ=850 N. Both cars are experiencing friction with coeffic of friction is 0.15
Transcript text: Two carts with masses $m_{1}=100 \mathrm{~kg}$ and $\mathrm{m}_{2}=50 \mathrm{~kg}$ are connected by the rope at the applied force of $\mathrm{F}_{\mathrm{a}}=850 \mathrm{~N}$. Both cars are experiencing friction with coeffic of friction is 0.15
Solution
Solution Steps
Step 1: Identify the Forces Acting on the System
The two carts are connected and pulled by an applied force Fa=850N. Both carts experience friction, which opposes the motion. The frictional force f for each cart can be calculated using the formula:
f=μ⋅m⋅g
where μ=0.15 is the coefficient of friction, and g=9.81m/s2 is the acceleration due to gravity.
Step 2: Calculate the Frictional Forces
For cart 1 with mass m1=100kg:
f1=μ⋅m1⋅g=0.15⋅100⋅9.81=147.15N
For cart 2 with mass m2=50kg:
f2=μ⋅m2⋅g=0.15⋅50⋅9.81=73.575N
Step 3: Calculate the Net Force and Acceleration
The net force Fnet acting on the system is the applied force minus the total frictional force:
Fnet=Fa−(f1+f2)=850−(147.15+73.575)=629.275N
The total mass of the system is m1+m2=100+50=150kg.
The acceleration a of the system can be calculated using Newton's second law:
a=m1+m2Fnet=150629.275=4.1952m/s2