Two adults and a child want to push a wheeled cart in thedirection marked x in Fig. 4.29 The two adults push with horizontalforces F_{1} and F_{2} as

BenoguigoliB 2021-02-05 Answered

Two adults and a child want to push a wheeled cart in thedirection marked x in Fig. 4.29 The two adults push with horizontalforces F1 and F2 as shown in the figure. (a)Find the magnitude and direction of the smallest force that thechild should exerts the minimum force found in part (a), the cartaccelerates at 2.0 ms2 in the +x direction. What is theweight of the cart?

You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Theodore Schwartz
Answered 2021-02-06 Author has 99 answers
a) The resultant must have no y-component, and sothe child must push with a force withy-component 140sin(30)100sin(60)=16.6N. For the child to exert the smallestpossible force, that force will have no x-component, so thesmallest possible force has magnitude 16.6 N and is at an angle of 270, or 90 clockwise from the +xdirection.
b) F=ma
m=Fa=140sin(30)+100sin(60)2=85.6kg
w=mg=(85.6)(9.8)=840N

We have step-by-step solutions for your answer!

Jeffrey Jordon
Answered 2021-09-30 Author has 2495 answers

a)Forces in the +y-direction:

F1y=100sin60=10032=86.6N

F2y=140sin30=1402=70N

So, the smallest force that the child should exert:

F=86.670=16.6N at 90 from +x clockwise (-y-direction).

b)Result forces in the +x-direction:

Fx=F1x+F2x=100cos60+140cos30=1002+14032=171.24N

The weight of the cart:

m=Fxa=171.242=85.62kg

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-01-06

A marble moves along the x-axis. The potential-energy functionis shown in Fig. 1
a) At which of the labeled x-coordinates is the force on the marble zero?
b) Which of the labeled x-coordinates is a position of stable equilibrium?
c) Which of the labeled x-coordinates is a position of unstable equilibrium?
image

asked 2021-02-19

 
Two snowcats tow a housing unit to a new location at McMurdo Base, Antarctica, as shown in the figure. The sum of the forces FA and FB exerted on the unit by the horizontal cables is parallel to the line L, and FA=4200 N. Determine FB? Determine the magnitude of FA+FB?

asked 2021-02-25

A stream of water strikes a stationary turbine bladehorizontally, as the drawing illustrates. The incident water streamhas a velocity of +18.0 m/s, while the exiting water stream has avelocity of -18.0 m/s. The mass of water per second that strikesthe blade is 17.0 kg/s. Find themagnitude of the average force exerted on the water by theblade.

asked 2021-01-31

A straight vertical wire carries a current of 1.20 A downward in a region b/t the poles of a large superconducting electromagnet,where the magnetic filed has magnitude B = 0.588 T and is horizontal. What are the magnitude and direction of the magnetic force on a 1.00 cm section of the wire that is in this uniform magnetic field, if the magnetic field direction is a) east? b)south? c) 30 degrees south of west?
According to the solutions, the force stays the same for parts a,b,c:F=IlB=7.06×103 but for part c,why isn't the 30 degree angle used to calculate the force?

asked 2021-02-11

A golf ball of mass 0.045 kg is hit off the tee at a speed of 45 m/s. The golf club was in contact with the ball for 5.0×103 s. Find (a) the impulse imparted to the golf ball,and (b) the average force exerted on the ball by the golf club.

asked 2020-12-03

A rectangular coil of wire, 22cm by 35 cm and carrying a current of 1.4A, is oriented with the plane of its loop perpendicular to a uniform 1.5T magnetic field. 
a) calculate the net force and torque which the magnetic field exerts on the coil. 
b)the coil is rotated through a 30 degree angle about the y axis, the left side coming out of the plane. Calculate the net force and torque which the magnetic field now exerts on the coil

asked 2022-08-16
Magnetic force acting on a current carrying wire
I am a high school student and I would like to know why in a magnetic field the Force, F, is equal to B I L sin ( θ ), where θ represents the angle between the magnetic field and the current. I understand that F is proportional to B, I and L, but I do not understand the inclusion of sin ( θ ). In other words, I would like to see a simple proof or explanation of why the effective length of the wire is L sin ( θ )

New questions